Skip to main content

A Portfolio of Minimum Risk in a Hybrid Uncertainty of a Possibilistic-Probabilistic Type: Comparative Study

  • Conference paper
  • First Online:
Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Abstract

We investigate a minimum risk portfolio model under conditions of a hybrid uncertainty of a possibilistic-probabilistic type with weak and strong triangular norms (t-norms) describing the interaction of fuzzy factors of the model. For the case of the weakest t-norm, a formula for variance is derived, which makes it possible to estimate the risk of the portfolio. An equivalent crisp analog of the model is constructed and demonstrated on a numerical example.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Yazenin, A.V.: Possibilistic-probabilistic models and methods of portfolio optimization. In: Batyrshin, I., Kacprzyk, J. et al. (eds.) Studies in Computational Intelligence, vol. 36, pp. 241–259. Springer, Heidelberg (2007). doi:10.1007/978-3-540-36247-0_9

  2. Xu, J., Zhou, X.: Fuzzy-Like Multiple Objective Decision Making. Studies in Fuzziness and Soft Computing, vol. 263. Springer, Berlin (2011). doi:10.1007/978-3-642-16895-6

    MATH  Google Scholar 

  3. Nahmias, S.: Fuzzy variables in a random environment. In: Gupta, M.M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Sets Theory and Applications, pp. 165–180. NHCP, Amsterdam (1979)

    Google Scholar 

  4. Puri, M.L., Ralescu, D.A.: Fuzzy Random Variables. J. Math. Anal. Appl. 114, 409–422 (1986). doi:10.1016/0022-247X(86)90093-4

    Article  MathSciNet  MATH  Google Scholar 

  5. Yazenin, A.V.: Basic Concepts of Possibility Theory: A Mathematical Apparatus for Decision-making Under Hybrid Uncertainty Conditions. Fizmatlit Publ. Moscow (2016). (in Russian)

    Google Scholar 

  6. Feng, Y., Hu, L., Shu, H.: The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets Syst. 120, 487–497 (2001). doi:10.1016/S0165-0114(99)00060-3

    Article  MathSciNet  MATH  Google Scholar 

  7. Dubois, D., Prade, H.: Théorie des Possibilités. Application à la Représentation des Connaissances en Informatique. Masson, Paris (1988)

    Google Scholar 

  8. Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. CRC Press, Boca Raton (1997)

    MATH  Google Scholar 

  9. Mesiar, R.: Triangular-norm-based addition of fuzzy intervals. Fuzzy Sets Syst. 91, 231–237 (1997). doi:10.1016/S0165-0114(97)00143-7

    Article  MathSciNet  MATH  Google Scholar 

  10. Hong, D.H.: Parameter estimations of mutually \(T\)-related fuzzy variables. Fuzzy Sets Syst. 123, 63–71 (2001). doi:10.1016/S0165-0114(00)00113-5

    Article  MathSciNet  MATH  Google Scholar 

  11. Yazenin, A.V., Soldatenko, I.S.: Possibilistic optimization tasks with mutually t-related parameters: solution methods and comparative analysis. In: Lodwick, W.A., Kacprzyk, J. (eds.) Studies in Fuzziness and Soft Computing, vol. 254, pp. 163-192. Springer (2010). doi:10.1007/978-3-642-13935-2_8

  12. Markowitz, H.M.: Portfolio selection. J. Finance 7(1), 77–91 (1952). doi:10.2307/2975974

    Google Scholar 

  13. Gordeev, R.N., Yazenin, A.V.: A method for solving a problem of possibilistic programming. J. Comput. Syst. Sci. Int. 45(3), 442–449 (2006). doi:10.1134/S1064230706030105

    Article  MathSciNet  MATH  Google Scholar 

  14. Yazenin, A.V.: Fuzzy and stochastic programming. Fuzzy Sets Syst. 22(1–2), 171–180 (1987). doi:10.1016/0165-0114(87)90014-5

    Article  MathSciNet  MATH  Google Scholar 

  15. Yazenin, A., Wagenknecht, M.: Possibilistic Optimization. Brandenburgische Technische Universitat, Cottbus (1996)

    MATH  Google Scholar 

  16. Yazenin, A.V.: On the problem of possibilistic optimization. Fuzzy Sets Syst. 81(1), 133–140 (1996). doi:10.1016/0165-0114(95)00245-6

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ilia Soldatenko .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Yazenin, A., Soldatenko, I. (2018). A Portfolio of Minimum Risk in a Hybrid Uncertainty of a Possibilistic-Probabilistic Type: Comparative Study. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 643. Springer, Cham. https://doi.org/10.1007/978-3-319-66827-7_51

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66827-7_51

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics